Optimal Time-Delay Control for Multi-Degree-of-Freedom Nonlinear Systems Excited by Harmonic and Wide-Band Noises

Abstract

In this paper, an optimal time-delay control strategy is designed for multi-degree-of-freedom (multi-DOF) strongly nonlinear systems excited by harmonic and wide-band noises. First, by using the generalized harmonic functions, a stochastic averaging method (SAM) is employed for the time-delay controlled strongly nonlinear system under combined harmonic and wide-band noise excitations, by which a set of partially averaged Itô equations are obtained. Then, by solving the dynamical programming equation associated with the partially averaged Itô equations, the optimal control law can be obtained. Finally, by solving the Fokker–Planck–Kolmogorov (FPK) equation, the responses of the optimally time-delay controlled system are predicted. The analytical results are compared with the Monte Carlo simulation to verify the effectiveness and efficiency of the proposed control strategy.

H‐infinity fault‐tolerant control for Markov jump system with actuator time delay

“…In order to stabilize those systems with time delays, many efforts have been made by scholars in recent years, and some stability analysis and controller design methods have been obtained. For example, an optimal time‐delay control strategy was designed by Hu and Lü [11] for multi‐degree‐of‐freedom strongly nonlinear systems, and by solving the Fokker–Planck–Kolmogorov equation, the responses of the optimally time‐delay controlled system were predicted. Mazare et al.…”

“…In order to stabilize those systems with time delays, many efforts have been made by scholars in recent years, and some stability analysis and controller design methods have been obtained. For example, an optimal time-delay control strategy was designed by Hu and Lü [11] for multi-degreeof-freedom strongly nonlinear systems, and by solving the Fokker-Planck-Kolmogorov equation, the responses of the optimally time-delay controlled system were predicted. Mazare et al [12] proposed an active fault tolerant control using adaptive fractional-based terminal back-stepping sliding mode control strategy for pitch angle control of a variable speed wind turbine, and simulation results were presented to reveal the effectiveness of the proposed controller.…”

Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation

“…Yang et al [33] analyzed the stability of a compressible laminated beam moving with variable velocity. In addition, on the problem of random vibration, Hu [34][35][36] analyzed the response and control for random time-delay systems under wide-band random excitations and Harmonic and Wide-Band Noises.…”

Finite-time energy-to-peak control for Markov jump systems with pure time delays

“…By using a time delay estimation algorithm, Mazare et al 2 proposed a method to design a fault-tolerant controller for a variable-speed wind turbine. By solving some special mathematical equations, Hu and Lü 3 designed a time-delay system control strategy for multi-DOF systems with strongly nonlinear characters. Additional results can be found in references.…”